II. THE MEANING AND APPLICATION OF STATISTICS AND STATISTICAL METHODS 1. The Meaning of Statistics and Statistical Methods Statistics is generally thought of from two points of view: first, as series of isolated numerical facts; and second, as methods involving the collecting, sorting, classifying, tabulating, summating, and comparing enumerated facts for the purpose of describing or explaining phenomena with which enumerations deal. Viewed solely in the first light, statistics is little more than arithmetic, and as such has little or no interest for us. From the second point of view, statistics closely approaches logic, concerned as it is with the processes and methods of formulating and testing conclusions from premises resting solely upon numerical bases. Obviously, however, the function, process, or method side, i.e. the application of methods of analysis in order to suggest the inferences and conclusions to be drawn cannot be divorced from the enumeration side, since it is the latter which helps to shape the premise the consequence of which it is desired to formulate. The conditions governing enumeration, such as the units and accuracy of measurements or enumeration, the completeness or representative character of the samples, etc., are vital and largely determine the methods to be employed in analysis. The adequacy of a tool, or the perfection of a machine, to speak analogously, is quite as important in the determination of a product as is the method of its utilization. However, skillful use may partly compensate for a poor tool, as skillful discrimination in statistical analysis may tend to counteract the error following from crude or defective enumeration. Statistics, as method, is as vitally concerned with enumeration as with the process and manner of analysis and synthesis, and in what follows the principles of methodology are extended to both phases of statistical study. 2 1 In definitions of statistics the emphasis has been variously placed. Bowley has called it the "science of averages" 1 as well as "the science of counting." The first definition emphasizes one device for statistical abbreviation; the other calls attention to the enumeration which precedes analysis. In another place, Bowley defines statistics as "numerical statements of facts in any department of inquiry, placed in relation to each other," and statistical methods as "devices for abbreviating and classifying the statements and making clear the relations." Yule defines statistics as "quantitative data affected to a marked extent by a multiplicity of causes," and statistical methods as "methods specially adapted to the elucidation of quantitative data affected by a multiplicity of causes.' Still others, using the terms with less precision, and in a less scientific sense, have sought to identify statistics with graphic methods to convert the science into an art. With the latter purpose we have little sympathy, yet due attention is later given to graphic methods as a means of statistical presentation. We shall use the term statistics as meaning aggregates of facts, "affected to a marked extent by a multiplicity of causes," numerically stated, enumerated, or estimated according to reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose, and placed in relation to each other. This definition seeks to emphasize the fact that before 3 Bowley, A. L., Elementary Manual of Statistics, p. 1. 4 Yule, G. U., An Introduction to the Theory of Statistics, p. 5. numerical data can be termed "statistics" they must bear evidence of having been collected in accordance with at least the rudiments of scientific method and for a definite purpose. It is necessary to insist that these conditions be fulfilled in order to know anything about the units of measurements employed and the scope and representativeness of the facts given numerical expression. Data not fulfilling these conditions may be numerical but they are not statistical. Too often "statistics" degenerate into "figures," and so-called "statistical bureaus" into nothing but "figure factories." Moreover, as Yule points out, "the term statistics is not usually applied to data, like those of the physicist, which are affected only by a relatively small residuum of disturbing causes." 1 Hence our reason for insisting, with Yule, upon the last-named condition. The requirement that statistics should conform to systematic and scientific methods of enumeration or estimation seems to connote the further condition that numerical facts are statistics only when "placed in relation to each other." 2 Stray and loose bits of information, gleaned here and there from indiscriminate sources, hearsay and unrelated material, while numerical in character, can be termed statistical only by a confused and unscientific use of terms. If they are capable of verification, if they take on homogeneity and assume regularity, then they may properly be classified as statistics. The expression statistical methods is used to include all those devices of analysis and synthesis by means of which statistics are scientifically collected and used to explain or describe phenomena either in their individual or related capacities. 1 Ibid. 2 Bowley, A. L., Elementary Manual of Statistics, p. 1. 2. The Application of Statistical Methods Statistics may be collected on most topics, but the employment of statistical methods in their study is not of universal nor of equal validity. At best the statistical is but one of many approaches in the explanation of phenomena. Its limitations are definite and certain, and its use in all cases should in no sense be considered valid. Statistics may often be used to corroborate conclusions arrived at by other methods, and it is in this respect, probably, that their greatest value lies. Many questions do not admit of statistical treatment at all; while respecting others, statistical considerations are of minor or of no consequence. The limitations of such methods are appreciated and clearly determined only after considerable experience, and it is one of the purposes of the volume to supply this training and experience. But this does not mean that their function is narrow and restricted. Both inside and outside of business, occasions are daily arising where statistical facts are indispensable as bases for decisions of policy, methods, etc. By means of them improvident and unbusiness-like methods may be detected, and new policies, savings, and projects suggested. The importance now assigned to proper methods of accounting and cost keeping in business is proof that this fact is being realized, and that definite knowledge of costs, profits, expenses, etc., is necessary to success. Accounting is concerned with the value aspect of these problems; statistics relates to the numerical or quantitative aspect whether value or some other unit is chosen as a measure of activity. These means of scientifically analyzing business are complementary. The need to-day is an appreciation of facts, an ability to observe the conditions which produce them, and a determination logically and scientifically to piece them together in such a way that they will serve as rules of business guidance. The problem, therefore, involves the establishment of units of measurements, analysis of activities according to these units, and the formulation of policies on the basis of the observations. The application of statistics and statistical methods to economic and to business problems is sufficiently emphasized, at this place, by merely calling attention to a few of the various fields in which they may be employed. The discussion, illustrations, and problems subsequently introduced serve definitely to bring out the detailed application. (1) Application within Business Units. a. Analysis of sales and sales possibilities by districts, by b. Analysis of production by departments, processes, etc. d. Analysis of production and factory organization. e. etc. (2) Application without and between Business Units. Affecting, a. Consumption (a) family budgets. (b) price phenomena. b. Production (a) capital and labor employed, the absolute amounts and |